Thermometry of stored molecular ion beams

The radiative cooling of a stored, initially rotationally hot OH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}- ion beam is probed by photodetachment using an electrostatic ion beam trap combined with an in-trap velocity map imaging spectrometer, providing direct measurement of the time-dependent rotational population. The rotational temperatures are estimated from photodetached electron spectra as a function of time using a Boltzmann distribution model and further verified by a rate law model using known Einstein coefficients. We demonstrate that during the entire cooling time, the rotational population can be well described by a Boltzmann distribution.

experiments 15,16 , it is more general, works over a larger range of temperatures, and provides a direct estimation of the rotational population during the entire storage time.
The photodetachment of OH − has been measured in a number of experiments [15][16][17][18][19][19][20][21][21][22][23] and its structure, energetic and potential energy surfaces have been calculated in several theoretical works 24 , and references therein. OH − ion is one of the most suitable candidates to explore photodetachment thermometry because the ground states of the anion and the neutral specie are dipole-bound states, the photodissociative potentials lie well above the photodetachment potentials 24,25 , and the rotational lines spacings are large, a feature particularly interesting for high resolution photoelectron spectra.

Results and experimental description
In the present experiment, a beam of OH − (electron affinity = 1.8277 eV 20 ) is produced in a Cs sputter ion source, accelerated to an energy of 4.2 keV and injected into an EIBT 7 . A schematic of the experimental setup is shown in Fig. 1. A velocity map imaging (VMI) set-up is installed in the field-free region, inside the EIBT to record the photoelectron spectra [26][27][28] . Once injected in the EIBT (where the pressure is about P = 2-3 × 10 −10 Torr), the stored particles oscillate between the two mirrors, with a lifetime of 435 ms. The measurement is stopped after 3 s, the residual stored beam is released by lowering the mirrors voltages, followed by a new injection for the next round of measurement.We estimate the ion number density by the DC ion current before the injection to the trap to be about 5 × 10 3 ions/cm 3 at the time zero and about 100 times less after 3 s (with or without the laser). The anions are crossed by a continuous wave (CW) laser beam with a photon energy of hν = 1.818 eV, at the middle of the VMI setup. The time of flight and position of the photodetached electrons are recorded by the VMI microchannel plate (MCP) detector, in coincidence with the resulting neutral OH, as detected by the MCP located outside the EIBT (see Fig 1). Each detector has an efficiency of about 50%. Coincidence efficiency is a multiplication of the detector efficiency divided by two (fragments counts only on one side of the trap), resulting in coincidence efficiency of about 12%. The VMI raw data for different trapping time ranges are shown in Fig. 2. The analysis starts, for each injection, after 100 ms of storage time to avoid complications due to unstable ion beam trajectories in the EIBT. As can be seen in Fig. 2, the size of the electron spot on the detector, which is directly related to the electron kinetic energy, is decreasing over time, suggesting that the initially hot OH − anions are cooling. Using well-known VMI analysis techniques, these images are first centralized, circularized, and then inverse Abel transformed 29  For convenience, a vertical shaded area is plotted, indicating the position of the distribution peak during the first time window (0.1-0.35 s). The negative data points observed at the latter storage time are the result of the background subtraction and the limited statistics available at these longer storage times.

Discussion
In order to extract the time-dependent temperature of the stored OH − , we assume that the electron kinetic energy distributions, for each time window, are the result of a thermal Boltzmann distribution of the OH − rotational states. To test this hypothesis, we use the well-known spectroscopic structural constants of OH and OH − 18,31 .
After electron detachment, the resulting neutral OH exhibits two states X 2 � 3/2 and X 2 � 1/2 due to spin-orbit coupling 17 . The corresponding transitions are labeled as '3' and '1' , respectively. Among all possible P3, P1, Q3, Q1, R3 and R1 transitions, the selected photon energy allows to probe only P3 and P1 transitions. An energy diagram representing anion to neutral transitions is shown in Fig. 3. Based on previous experiments 17, 30 , it is known that the initial population of vibrational excited states of OH − is negligible. Also, using the calculated dipole moment of OH − , the estimated lifetime of the v = 1 state is of the order of 7 ms 25 , which is much smaller than the time delay between the beam injection and the start of the measurement (100 ms). Using j-dependent   15,20 ).
kT where T is the molecular rotational temperature and E j and C(j, T) are the rotational energy and the relative population of the j level of OH − , the total intensities, I j , of P3 and P1 transitions can be estimated as 15,16 (1) I j = NÎ j (hν − hν j ) a * C(j, T)  www.nature.com/scientificreports/ where hν , hν j and a are the photon energy, the transition energies for P3 and P1 transitions and the Wigner factor, respectively. In this study, a is set to 0.2 15 , and N is a normalization constant. Although the partition function is temperature dependent, it has only a constant value for a given temperature (implicitly included in the normalization factor). Since we use only relative populations it does not affect the extracted temperature when the area under the distribution is normalized to unity (as was done in this work). In order to fit the experimental data shown in Fig. 4, the distribution of rotational level energies are converted to a distribution of electron kinetic energies by energy conservation: where hν (j) are the energies for P3 and P1 transitions written in terms of OH − rotational levels j. hν (j) is calculated using the electron affinity and the rotational level energies of OH − and X 2 � 3/2 and X 2 � 1/2 states of OH, including selection rules. Using Eqs. (1) and (2), the photodetached electron spectrum (PDES) shown in Fig. 4 is fitted with T as a free parameter (and N as a normalization factor), and shown as a green dotted line. As can be seen, the assumption that the electron kinetic energy is the result of a Boltzmann distribution for the rotational state of OH − yields a reasonable fit to the experimental data, for most of the storage time windows, although there are visible discrepancies, especially during the first second of storage.
The resulting fitted temperatures T are plotted as a function of time in Fig. 5, shown by green dots. These results demonstrate the rapid cooling of the rotational states of the stored OH − over the 3 s of storage, starting from a temperature of about 5100 K for the initial time window of 0.1-0.35 s down to about 800 K after 2.75 s of storage. Note that the fitted initial temperature, 5100 ± 200 K in this study is in consistence with the estimated initial temperature of 6000 ± 2000 K by Meyer et al. 15 , where the molecular ions were produced in a similar ion source.
To support the analysis of the data shown in Fig. 4 we compare the results shown in Fig.5 to the expected cooling rate obtained from the known Einstein coefficients of OH − . To perform such an analysis, the time-dependent population P j of OH − rotational level j is calculated using the following Master equation: where A j , B ′ j and B j are the Einstein coefficients in the units of s −1 between j and j − 1 rotational levels, namely spontaneous emission, stimulated emission and photon absorption, respectively. The later two processes take place due to the thermal blackbody radiation from the EIBT environment. Given that the experiment is performed at room temperature, the blackbody spectrum is calculated at 300 K.
In order to solve Eq. (3), the initial rotational state population (temperature) for the first time window [0.1-0.35] s is assumed to be identical to the one extracted in the analysis above. Up to 50 rotational states are , which can then be used to create "synthetic" electron energy spectra, to be compared to the experimental data shown in Fig. 4 as solid red lines. A better agreement than the one assuming a simple Boltzmann distribution (green dotted lines) is obtained between this model and the experimental data. Note that except for the initial population, there are no fitting parameters in this model, supporting the theoretical values for the Einstein coefficients and the spectroscopic constants 22,32,33 , within the experimental resolution.
To provide an overall comparison between the photoelectron spectrum model and the Master equation (Eq. 3), a time-dependent temperature can be extracted from the solution of the differential equations by fitting them to a Boltzmann distribution. The results are shown in Fig. 5 as red and blue dots. The agreement with the analysis performed under the assumption that the data can be represented by a Boltzmann distribution at all time (green dots) is very reasonable, demonstrating the validity of such an assumption. Also shown in Fig. 5 (red dots) is the solution of Eq. (3) with the effect of blackbody radiation (i.e., including all Einstein coefficients A j , B j and B ′ j ). As expected, given the relatively high temperature of the molecular ions at the beginning of the measurement (5100 K) and at the end (800 K), the influence of spontaneous emission is most significant. Nevertheless, as the rotational cooling takes place, and the temperature decreases, the effect of the blackbody radiation becomes visible, and the calculated cooling rate decreases. The Master equation was checked by calculating that, for much longer storage time, the rotational population indeed reaches the expected value for 300 K when blackbody radiation is included, and 0 K (i.e., only the j = 0 state being populated) when B j = B ′ j = 0.

Conclusion
In conclusion, the relaxation behavior of rotationally hot OH − has been measured using a combined method of photodetachment, ion beam storage, and electron spectrometry. We demonstrate that in the case of OH − , the population distribution can be reasonably well described by a Boltzmann distribution. Such method can be useful to estimate the internal population of stored ions in rings or traps where molecular reactions are taking place. The method can be used to provide information on, or comparison with Einstein coefficients, and provide a direct view of the internal dynamics of the relaxation process within a molecular anion. Additionally, such a tool can be very useful for probing the cooling of atomic clusters or polycyclic aromatic hydrocarbons (PAHs), as it provides a direct image of the internal relaxation process as a function of time, and deviation from the simple Boltzmann distribution can be clearly observed.

Data availability
The experimental data used and analyses methodologies during the current study are available from the corresponding author on reasonable request.